Specify the inheritance of location, rotation, scale when parenting objects
Copy Location Constraint

Blender has a copy location, rotation and scale constraint, as well as a copy transform constraint (ie copy all three_)  Adding all of location, rotation and scale, or copy transform with influence 1 and using world space is the equivalent of parenting.

For question example consider adding just  a copy location constraint on A targeting B


Example default Cube at location of default Camera. With offset unchecked is at exact global location. With it checked will behave similarly to a child, and be offset from parent based on its location

Leaving above the same: If we add another copy location constraint, targeting the Light, with influence 1, the cube will be at location of Light. With influence 0.5 will be half way between Camera and Light.